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# Interest rates model

This page describes how Equilibrium calculates interest rates on the loans in the system.

## Pricing

The problem of pricing a collateralised loan comes from the realms of traditional finance and stock loans. Associated research on this was pioneered by Xia and Zhou (2007). Under the Black–Scholes model, they derived a closed-form pricing formula for the infinite-maturity stock loan by solving the related optimal stopping problem. Equilibrium adapts the approach proposed by Xia and Zhou, and comes up with an elegant pricing solution that depends on borrower portfolio risk and the level of portfolio collateralization.
$Interest\ rate \approx Leverage * (Portfolio\ volatility * Scale\ factor)$
The interest that borrowers pay gets redistributed across the system components. The following breakdown applies:
Interest rate component
Value
Base Lender Rate
0.5% APR
Base Insurance Rate
1.0% APR
Base Treasury Rate
1.0% APR
Primary Borrower Rate
~ Leverage * Volatility
Lender share
30% of Primary Borrower Rate
Bailsman share
70% of Primary Borrower Rate
So the minimum possible interest rate borrowers pay is 2.5% APR, while the biggest contributor to the final interest rate figure is the Primary Borrower Rate which depends on the leverage the borrower undertakes and the risk (volatility) of the borrower portfolio. 30% of the Primary Borrower Rate is funnelled to lenders, while 70% is funnelled to insurers (bailsmen).
The base treasury rate is split among treasury and collators in a 50 / 50 proportion, so collators earn a 0.5% APR on top of their trx. fees rewards. Assuming the default values for risk parameters, here's the approximate interest rate breakdown (how much borrowers pay to bailsmen and lenders respectively) for a borrower portfolio, given its leverage and volatility. How much borrower pays to bailsmen and lenders given the leverage and portfolio risk (volatility)
Further improvements to the pricing model may include adapting the jump diffusion process to model the collateral risk, as well as adapting the model to account for margin calls and LTV requirements. This is subject of our ongoing R&D work.